Question

Construct a quadrilateral ABCD whose sides are AB = 4 cm, BC = 5 cm, CD = 4.5 cm, ∠B = 60° and ∠C = 90°.

Answer 1

First of all we draw a rough sketch of the required quadrilateral and write down the given dimensions.

Steps of Construction

1. We draw EA = 5 cm.
2. Then we make ∠XEA = 60°

3. With E as centre and radius 4 cm, we cut off ED = 4 cm along EX.

4. Now we make ∠EAY = 90°

5. With A as centre and radius 4.5 cm, we draw an arc to cut off AY at R.

6. At the end, we join DR.

Hence DEAR is the required quadrilateral.